Antoni.

That is a tough one, I'm just going to put Joey because it would be weird for his father to die and someone else to take over the family, which is his lastname. Why would Joey Leone be answering to Toni Cipriani, head of the Leone family? Plus it doesn't look like Toni is having any problems being a capo.

MyDog

When a boss dies, either his son takes over or the high-ranking members vote for the new boss. Even if Joey took over, do you really think Toni would accept answering to him? Toni probably has more popularity and influence with other members than Joey. Toni would just kill him and take over.

Darth_Starkiller

Honestly, I believe Joey wouldn't accept beind the don and allow Toni to take it. Not only he doesn't seem fit for it, he also doens't seem like he wants. And if he did, most likely he'd die and be replaced by Toni soon or be kind of Toni's puppet.